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Abstract

We propose a two dimensional (2D) photonic crystal (PhC) structure that supports super-collimation over a large frequency range (over 4 times that of a traditional square lattice of holes). We theoretically and numerically investigate the collimation mechanism in our 2D structure, in comparison to that of two other frequently used related PhC structures. We also point out the potential importance of our proposed structure in the design of super-collimation-based devices for both monochromatic and polychromatic light.

As explained in [21], one could embed a slab of our proposed 2D PhC into a 3D PhC having a complete photonic bandgap, and design things in such a way that the extended frequency range supporting supercollimation falls inside the complete bandgap of the 3D PhC. This would prevent radiation losses from the ‘slab version’ of our proposed 2D PhC structure.

Other (4)

As explained in [21], one could embed a slab of our proposed 2D PhC into a 3D PhC having a complete photonic bandgap, and design things in such a way that the extended frequency range supporting supercollimation falls inside the complete bandgap of the 3D PhC. This would prevent radiation losses from the ‘slab version’ of our proposed 2D PhC structure.

Figures (3)

Two “often-used” low-diffraction structures. (a) Profile of the refractive index of a 2D holes-in-dielectric structure, with the dielectric having n = 3.5, and the holes having radius r = 0.421a′, where a′ is the nearest-neighbor center-to-center separation between holes (the square lattice spacing). Note that the holes form a square lattice. (b) Color contour plot of the frequency of the first TE band for the structure shown in Fig. 1(a). (c) Profile of the refractive index for a waveguide array structure, with the waveguide having refractive index n = 3.5. (d) Projected band diagram of the first TM band for the waveguide array with t = 0.2a. (e) Color contour plot of the frequency of the first TM band for the waveguide array with t = 0.2a.

Proposed 2D PhC structure (a) Schematic of the refractive index: the rods, of radius r, and waveguides, of thickness t, (shown in green) both have n = 3.5, and are surrounded by air (n = 1). The rods form a square lattice, with lattice constant a, and the waveguides are halfway (on the y-axis) between the rods. (b) Projected band diagram of lowest four TM bands for r = 0.16; and t = 0.2a. (c) Color contour plot of the frequency of the fourth TM band.

Intensity profile of the propagating beam (of angular frequency 0.495 (2πc/a), and physical width corresponding to σky = 0.12(2π/a)) as a function of y(a), at x = 0 (in blue) and at i = 500a (in red), in (a) Our proposed PhC structure shown in Fig. 2, (b) The 2D holes structure shown in Fig. 1(a), but with lattice constant a′ = (0.2124/0.495)a, where a is the lattice constant in our proposed structure and in the waveguide array structures, (c) The waveguide array structure with t = 0.2a. Note that the spikes in (a) and (c) correspond to the positions of the “waveguide” strips.